What we ultimately want to accomplish is to have all programs and files centralized so everyone can acces them.
You pretty much have this through your fourth computer with your files. I do not think you would receive any benefit having your programs running from central computer. You could do it but with a substanical expense. Having a common computer with the data files stored on it would be the easiest and most cost efficiant. Unless you want to learn how to configure and maintain a server. You may even want to look at a NAS (Network Attached Storage). It is a hard drive that is housed it it's own case and simply plugged into your LAN.
I would also recommend you have 2 hard drives one as a backup in the event the first fails. It is refered to as "Mirroring". It is a form of backup that you can do with simple backup software.
This can be done with new purpose bought hardware\software or use an old computer setup to share it's directories with the others on the LAN.
Also we are thinking about going "paperless", so a lot of paper files will have to be scanned into the system. I'm not sure if this makes a difference, but I know PDF files tend to be big. We all have internet access through a cable modem attached to a wireless router. Currently our PCs (3) are running on Windows XP, and one laptop on XP - they are all connected via the wireless router.
I would like to make a suggestion, and it is my personal preference. I would wire all my computers and move away from wireless, unless the topographic of your office makes it impractical. While wireless networks can be very secure I still rather hard wired computers and devices where possible.
If these .pdf files are to be available in a database (Fill in the blank) you may not have a choice but to setup a server instead on simple fire sharing.
The size of the .pdf files is only an issue as far as the amount of available hard drive pace on your LAN. With hard drives getting bigger ever month that is limited only by your budget. You can buy 1 terabyte hard drives now (1 Tb = 1024 Gb).
I hope this helps.